Classical and quantum dynamics of confined test particles in brane gravity

A model is constructed for the confinement of test particles moving on a brane. Within the classical framework of this theory, confining a test particle to the brane eliminates the effects of extra dimensions, rendering them undetectable. However, in the quantized version of the theory, the effects of the gauge fields and extrinsic curvature are pronounced and this might provide a hint for detecting them. As a consequence of confinement the mass of the test particle is shown to be quantized. The condition of stability against small perturbations along extra dimensions is also studied and its relation to dark matter is discussed.